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3753. Total Waviness of Numbers in Range II

Description

You are given two integers num1 and num2 representing an inclusive range [num1, num2].

The waviness of a number is defined as the total count of its peaks and valleys:

  • A digit is a peak if it is strictly greater than both of its immediate neighbors.
  • A digit is a valley if it is strictly less than both of its immediate neighbors.
  • The first and last digits of a number cannot be peaks or valleys.
  • Any number with fewer than 3 digits has a waviness of 0.

Return the total sum of waviness for all numbers in the range [num1, num2].

Β 

Example 1:

Input: num1 = 120, num2 = 130

Output: 3

Explanation:

In the range [120, 130]:

  • 120: middle digit 2 is a peak, waviness = 1.
  • 121: middle digit 2 is a peak, waviness = 1.
  • 130: middle digit 3 is a peak, waviness = 1.
  • All other numbers in the range have a waviness of 0.

Thus, total waviness is 1 + 1 + 1 = 3.

Example 2:

Input: num1 = 198, num2 = 202

Output: 3

Explanation:

In the range [198, 202]:

  • 198: middle digit 9 is a peak, waviness = 1.
  • 201: middle digit 0 is a valley, waviness = 1.
  • 202: middle digit 0 is a valley, waviness = 1.
  • All other numbers in the range have a waviness of 0.

Thus, total waviness is 1 + 1 + 1 = 3.

Example 3:

Input: num1 = 4848, num2 = 4848

Output: 2

Explanation:

Number 4848: the second digit 8 is a peak, and the third digit 4 is a valley, giving a waviness of 2.

Β 

Constraints:

  • 1 <= num1 <= num2 <= 1015​​​​​​​

Solutions

Solution 1

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static int len, digits[20];
static long long memoCnt[20][11][11][2];
static long long memoSum[20][11][11][2];
static char vis[20][11][11][2];
static long long cnt, sum;

static void dfs(int pos, int pp, int pr, int st, int ti) {
    if (pos == len) {
        cnt = 1;
        sum = 0;
        return;
    }
    if (!ti && vis[pos][pp][pr][st]) {
        cnt = memoCnt[pos][pp][pr][st];
        sum = memoSum[pos][pp][pr][st];
        return;
    }
    int h = ti ? digits[pos] : 9;
    long long c = 0, s = 0;
    for (int d = 0; d <= h; d++) {
        int ns = st || d;
        long long a = 0;
        int npp, np;
        if (!ns) {
            npp = 10;
            np = 10;
        } else if (!st) {
            npp = 10;
            np = d;
        } else {
            if (pp != 10 && pr != 10 && ((pr > pp && pr > d) || (pr < pp && pr < d)))
                a = 1;
            npp = pr;
            np = d;
        }
        dfs(pos + 1, npp, np, ns, ti && d == h);
        c += cnt;
        s += sum + a * cnt;
    }
    if (!ti) {
        vis[pos][pp][pr][st] = 1;
        memoCnt[pos][pp][pr][st] = c;
        memoSum[pos][pp][pr][st] = s;
    }
    cnt = c;
    sum = s;
}

static long long calc(long long N) {
    if (N < 0) return 0;
    len = 0;
    long long x = N;
    if (!x) {
        digits[len++] = 0;
    } else {
        char buf[20];
        int l = 0;
        while (x) {
            buf[l++] = x % 10;
            x /= 10;
        }
        for (int i = l - 1; i >= 0; i--)
            digits[len++] = buf[i];
    }
    memset(vis, 0, sizeof(vis));
    dfs(0, 10, 10, 0, 1);
    return sum;
}

long long totalWaviness(long long a, long long b) {
    return calc(b) - calc(a - 1);
}

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